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In this paper, we propose a reinforced Blocking Matrix of TF-GSC by incorporating a cross channel projection for speech enhancement. Transfer function GSC (TF-GSC) proposed by Gannot was aimed at improving speech quality but the desired speech signal becomes somewhat distorted since the reference signal resulting from blocking matrix significantly contains the desired signal. The proposed reinforcement on the Blocking Matrix is a scheme to remove the highly correlated components between the inter-channel reference signals using orthogonal projection, thereby completely eliminating the desired signal. Representative experiments show that the proposed scheme is effective and its strength is demonstrated in terms of improved averaged signal noise ratio(SNR) and Log Spectral Distance(LSD).